Skip to main content

Exact Algorithms for the Chance-Constrained Vehicle Routing Problem

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9682)

Abstract

We study the chance-constrained vehicle routing problem (CCVRP), a version of the vehicle routing problem (VRP) with stochastic demands, where a limit is imposed on the probability that each vehicle’s capacity is exceeded. A distinguishing feature of our proposed methodologies is that they allow correlation between random demands, whereas nearly all existing methods for the stochastic VRP require independent demands. We first study an edge-based formulation for the CCVRP, in particular addressing the challenge of how to determine a lower bound on the number of trucks required to serve a subset of customers. We then investigate the use of a branch-and-cut-and-price (BCP) algorithm. While BCP algorithms have been considered the state of the art in solving the deterministic VRP, few attempts have been made to extend this framework to the stochastic VRP.

Keywords

  • Customer Demand
  • Vehicle Rout Problem
  • Chance Constraint
  • Random Demand
  • Price Subproblem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-33461-5_8
  • Chapter length: 13 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   64.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-33461-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   84.99
Price excludes VAT (USA)

Notes

  1. 1.

    Note that \(\mathbb {P}\{ D(S) \le b\} \ge 1-\epsilon \iff Q_{1-\epsilon }( D(S) ) \le b\).

References

  1. Baldacci, R., Mingozzi, A.: A unified exact method for solving different classes of vehicle routing problems. Math. Program. 120(2), 347–380 (2009)

    MathSciNet  CrossRef  MATH  Google Scholar 

  2. Baldacci, R., Mingozzi, A., Roberti, R.: New route relaxation and pricing strategies for the vehicle routing problem. Oper. Res. 59(5), 1269–1283 (2011)

    MathSciNet  CrossRef  MATH  Google Scholar 

  3. Bertsimas, D.J.: A vehicle routing problem with stochastic demand. Oper. Res. 40(3), 574–585 (1992)

    MathSciNet  CrossRef  MATH  Google Scholar 

  4. Christiansen, C.H., Lysgaard, J., Wøhlk, S.: A branch-and-price algorithm for the capacitated arc routing problem with stochastic demands. Oper. Res. Lett. 37(6), 392–398 (2009)

    MathSciNet  CrossRef  MATH  Google Scholar 

  5. Christofides, N., Mingozzi, A., Toth, P.: Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations. Math. Program. 20(1), 255–282 (1981)

    MathSciNet  CrossRef  MATH  Google Scholar 

  6. Clarke, G., Wright, J.W.: Scheduling of vehicles from a central depot to a number of delivery points. Oper. Res. 12(4), 568–581 (1964)

    CrossRef  Google Scholar 

  7. Contardo, C., Martinelli, R.: A new exact algorithm for the multi-depot vehicle routing problem under capacity and route length constraints. Discr. Optim. 12, 129–146 (2014)

    MathSciNet  CrossRef  MATH  Google Scholar 

  8. Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Man. Sci. 6(1), 80–91 (1959)

    MathSciNet  Google Scholar 

  9. Dror, M., Laporte, G., Louveaux, F.V.: Vehicle routing with stochastic demands and restricted failures. Zeitschrift für Oper. Res. 37(3), 273–283 (1993)

    MathSciNet  MATH  Google Scholar 

  10. Fukasawa, R., Longo, H., Lysgaard, J., de Aragão, M.P., Reis, M., Uchoa, E., Werneck, R.F.: Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Math. Program. 106(3), 491–511 (2006)

    MathSciNet  CrossRef  MATH  Google Scholar 

  11. Gauvin, C., Desaulniers, G., Gendreau, M.: A branch-cut-and-price algorithm for the vehicle routing problem with stochastic demands. Comput. & Oper. Res. 50, 141–153 (2014)

    MathSciNet  CrossRef  Google Scholar 

  12. Irnich, S., Desaulniers, G.: Shortest path problems with resource constraints. In: Desaulniers, G., Desrosiers, J., Solomon, M. (eds.) Column Generation. Springer, New York (2005)

    Google Scholar 

  13. Laporte, G., Louveaux, F., Mercure, H.: Models and exact solutions for a class of stochastic location-routing problems. European J. Oper. Res. 39(1), 71–78 (1989)

    MathSciNet  CrossRef  MATH  Google Scholar 

  14. Laporte, G., Louveaux, F., Mercure, H.: The vehicle routing problem with stochastic travel times. Trans. Sci. 26(3), 161–170 (1992)

    CrossRef  MATH  Google Scholar 

  15. Laporte, G., Louveaux, F.V., Van Hamme, L.: An integer L-shaped algorithm for the capacitated vehicle routing problem with stochastic demands. Oper. Res. 50(3), 415–423 (2002)

    MathSciNet  CrossRef  MATH  Google Scholar 

  16. Luedtke, J., Ahmed, S.: A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19, 674–699 (2008)

    MathSciNet  CrossRef  MATH  Google Scholar 

  17. Pecin, D., Pessoa, A., Poggi, M., Uchoa, E.: Improved branch-cut-and-price for capacitated vehicle routing. In: Lee, J., Vygen, J. (eds.) IPCO 2014. LNCS, vol. 8494, pp. 393–403. Springer, Heidelberg (2014)

    CrossRef  Google Scholar 

  18. Secomandi, N., Margot, F.: Reoptimization approaches for the vehicle-routing problem with stochastic demands. Oper. Res. 57(1), 214–230 (2009)

    CrossRef  MATH  Google Scholar 

  19. Song, Y., Luedtke, J.R., Küçükyavuz, S.: Chance-constrained binary packing problems. INFORMS J. Comput. 26(4), 735–747 (2014)

    MathSciNet  CrossRef  MATH  Google Scholar 

  20. Stewart, W.R., Golden, B.L.: Stochastic vehicle routing: a comprehensive approach. Euro. J. Oper. Res. 14(4), 371–385 (1983)

    CrossRef  MATH  Google Scholar 

  21. Yang, W.H., Mathur, K., Ballou, R.H.: Stochastic vehicle routing problem with restocking. Trans. Sci. 34(1), 99–112 (2000)

    CrossRef  MATH  Google Scholar 

Download references

Acknowledgments

Fukasawa was supported by NSERC Discovery Grant RGPIN-05623. Luedtke was supported by NSF grants CMMI-0952907 and CMMI-1130266, and ONR award N00014-15-1-2268.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Ricardo Fukasawa or James Luedtke .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Dinh, T., Fukasawa, R., Luedtke, J. (2016). Exact Algorithms for the Chance-Constrained Vehicle Routing Problem. In: Louveaux, Q., Skutella, M. (eds) Integer Programming and Combinatorial Optimization. IPCO 2016. Lecture Notes in Computer Science(), vol 9682. Springer, Cham. https://doi.org/10.1007/978-3-319-33461-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-33461-5_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33460-8

  • Online ISBN: 978-3-319-33461-5

  • eBook Packages: Computer ScienceComputer Science (R0)